leanprover-community / leanprover-community/mathlib4
Hermite functions
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Description
https://leanprover-community.github.io/mathlib4_docs/Mathlib/Analysis/SpecialFunctions/Gaussian/FourierTransform.html#fourierIntegral_gaussian_pi gives the Fourier Transform of a Gaussian
https://github.com/leanprover-community/mathlib4/tree/master/Mathlib/RingTheory/Polynomial/Hermite defines the Hermite polynomials
Missing are:
- Hermite functions (continuity, IsBigO, Schwartz)
- their Fourier transforms as eigenfunctions and diagonalisation of the Fourier transform as an orthogonal basis of L^2(R)
- Hermite polynomials as a sequence of orthogonal polynomials under the gaussian measure
Contributor guide
First steps
- Read the whole issue, then the project's contributing guide.
- Comment on the issue to say you are picking it up — it saves two people doing the same work.
- Fork the repository and make your change on a branch.
- Open a pull request that references the issue number.
Research direction
Start with Mathlib/RingTheory/Polynomial/Hermite and the linked Gaussian Fourier-transform documentation to understand the existing definitions and results. The requested work spans Hermite functions, Fourier eigenfunctions, L2 diagonalisation, and Gaussian orthogonality. Done means the listed missing mathematical results are formalized in the library.
Written by the indexing model from the issue text.
Assessment
- Domain
- backend
- Issue type
- Feature
- Difficulty
- 5/5
- Estimated time
- Over a week
- Activity status
- Stale
- Clarity
- Needs clarification
- Newbie friendliness
- 20/100